A certain spring is compressed 0.2 metres from its natural length by a force of 0.02...

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Physics

A certain spring is compressed 0.2 metres from its naturallength by a force of 0.02 newtons. A 0.1 kilogram mass is attachedto this spring. There is no damping, and the mass is acted on by anexternal force of 0.05 cos(0.8 t) newtons, where t is measured inseconds. At t = 0, the mass is released, at rest, from its rest(equilibrium) position.
(a) Set up and solve the initial value problem for thedisplacement x(t) of the mass from its rest (equilibrium) position,where x is measured in metres. Express x(t) as a sum of sinusoidal(i.e. sine or cosine) functions of t.
(b) Express x(t) from part (a) as a product of sinusoidalfunctions of t, and identify the two â€œenvelopeâ€ functions that x(t)oscillates between.

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3.8 Ratings (547 Votes)

First it is neccesary to obtain the value of the springconstantThen according to Newtons second law without dampingforceaThe differential equation See Answer

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